PHYS 5326 – Lecture #9 & 10

1. PHYS 5326 – Lecture #9 & 10 Friday, Feb. 21, 2003 Dr. JaeYu • Interpretation of Sin2qW results • The link to Higgs • Neutrino Oscillation • Next makeup class is Friday, Mar. 14, 1-2:30pm, rm 200. PHYS 5326, Spring 2003 Jae Yu

2. SM Global Fits with New Results Without NuTeV c2/dof=20.5/14: P=11.4% With NuTeV c2/dof=29.7/15: P=1.3% Confidence level in upper Mhiggs limit weakens slightly. LEP EWWG: http://www.cern.ch/LEPEWWG PHYS 5326, Spring 2003 Jae Yu

3. Tree-level Parameters: r0 and sin2qW(on-shell) • Either sin2qW(on-shell) or r0 could agree with SM but both agreeing simultaneously is unlikely PHYS 5326, Spring 2003 Jae Yu

4. Model Independent Analysis • Rn(`n) can be expressed in terms of quark couplings: • Where • Paschos-Wolfenstein formula can be expressed as PHYS 5326, Spring 2003 Jae Yu

5. From two parameter fit to and Model Independent Analysis • Performed a fit to quark couplings (and gL andgR) • For isoscalar target, the nN couplings are (SM: 0.3042 -2.6s deviation) (SM: 0.0301  Agreement) PHYS 5326, Spring 2003 Jae Yu

6. Model Independent Analysis Difficult to explain the disagreement with SM by: Parton Distribution Function or LO vs NLO or Electroweak Radiative Correction: large MHiggs PHYS 5326, Spring 2003 Jae Yu

7. What is the discrepancy due to (Old Physics)? • R- technique is sensitive to q vs`q differences and NLO effect • Difference in valence quark and anti-quark momentum fraction • Isospin symmetry assumption might not be entirely correct • Expect violation about 1%  NuTeV reduces this effect by using the ratio of n and `ncross sections  Reducing dependence by a factor of 3 PHYS 5326, Spring 2003 Jae Yu

8. What is the discrepancy due to (Old Physics)? • s vs`s quark asymmetry • s and `s needs to be the same but the momentum could differ • A value of Ds=xs -x`s ~+0.002 could shift sin2qW by -0.0026, explaining ½ the discrepancy (S. Davison, et. al., hep-ph/0112302) • NuTeV di-m measurement shows that Ds~-0.0027+/-0.0013 Use opposite sign di-m events to measure s and `s. PHYS 5326, Spring 2003 Jae Yu

9. What is the discrepancy due to (Old Physics)? • NLO and PDF effects • PDF, mc, Higher Twist effect, etc, are small changes • Heavy vs light target PDF effect (Kovalenko et al., hep-ph/0207158) • Using PDF from light target on Iron target could make up the difference  NuTeV result uses PDF extracted from CCFR (the same target) PHYS 5326, Spring 2003 Jae Yu

10. If nens with nens Oscillations with Large Mn • LSND result implicate a large Dm2 (~10 — 100eV2) solution for ne oscillation MiniBooNe at FNAL is running to put the nail on the coffin • How would this affect NuTeV sin2qW? and then Thus, MC will subtract more than it is in nature, causing measured Rn to be smaller and thereby increasing sin2qW PHYS 5326, Spring 2003 Jae Yu

11. New Physics: Interactions from Extra U(1) – Z’ • Extra U(1) gauge group giving rise to interactions mediated by heavy Z’ boson (MZ’>>MZ) • While couplings in these groups are arbitrary, E(6) gauge groups can provide mechanism for extra U(1) interaction via heavy Z’. • Can give rise to gR but not gL which is strongly constrained by precision Z measurement PHYS 5326, Spring 2003 Jae Yu

12. Both precision data are lower than SM What other explanations (New Physics)? • Heavy non-SM vector boson exchange: Z’, LQ, etc • Suppressed Znn (invisible) coupling • LL coupling enhanced than LR needed for NuTeV PHYS 5326, Spring 2003 Jae Yu

13. What other explanations (New Physics)? • Propagator and coupling corrections • Small compared to the effect • MSSM : Loop corrections wrong sign and small for the effect • Many other attempts in progress but so far nothing seems to explain the NuTeV results • Lepto-quarks • Contact interactions with LL coupling (NuTeV wants mZ’~1.2TeV, CDF/DØ: mZ’>700GeV) • Almost sequential Z’ with opposite coupling to n Langacker et al, Rev. Mod. Phys. 64 87; Cho et al., Nucl. Phys. B531, 65; Zppenfeld and Cheung, hep-ph/9810277; Davidson et al., hep-ph/0112302 PHYS 5326, Spring 2003 Jae Yu

14. Linking sin2qW with Higgs through Mtop vs MW One-loop correction to sin2qW PHYS 5326, Spring 2003 Jae Yu

15. Neutrino Oscillation • First suggestion of neutrino mixing by B. Pontecorvo at the K0, K0-bar mixing in 1957 • Solar neutrino deficit in 1969 by Ray Davis in Homestake Mine in SD.  Called MSW effect • Caused by the two different eigenstates for mass and weak • Neutrinos change their flavor as they travel  Neutrino flavor mixing • Oscillation probability depends on • Distance between the source and the observation point • Energy of the neutrinos • Difference in square of the masses PHYS 5326, Spring 2003 Jae Yu

16. where and are weak eigenstates, while and are mass eigenstates, and q is the mixing angle that give the extent of mass eigenstate mixture, analogous to Cabbio angle Neutrino Oscillation Formalism • Two neutrino mixing case: OR PHYS 5326, Spring 2003 Jae Yu

17. Oscillation Probability • Let nm at time t=0 be the linear combination of n1 and n2 with masses m1 and m1, the wave function becomes: • Then later time t the nm wave function becomes: • For relativistic neutrinos (En>>mi), the energies of the mass eigenstates are: PHYS 5326, Spring 2003 Jae Yu

18. where and . Oscillation Probability • Substituting the energies into the wave function: • Since the n’s move at the speed of light, t=x/c, where x is the distance to the source of nm. • The probability for nm with energy En oscillates to ne at the distance L from the source becomes PHYS 5326, Spring 2003 Jae Yu

19. Homework Assignments • Produce an electron ET spectrum of the highest ET electrons in your samples • Due Wednesday, Feb. 26 • Complete the derivation of the probability for nm of energy En to oscillate to ne at the distance L away from the source of nm. • Draw the oscillation probability distributions as a function of • Distance L for a fixed neutrino beam energy En (=5, 50, 150 GeV) • En for a detector at a distance L (=1.5, 735, 2200km)away from the source • Due Wednesday, Mar. 5 PHYS 5326, Spring 2003 Jae Yu